I'm currently a senior at BYU, so I thought I could give some information for interested applicants.

Culture: The department is a little small but very close-knit. You're looking at somewhere around 30 professors with active research groups, probably 200-250 undergraduates (including the ones who don't survive past freshman year), and around 30 graduate students. Despite the small graduate program, there's a lot of research going on because of an undergraduate thesis requirement that amounts to ~2 years of research (most professors have about three to five undergraduate students, but some very brave professors may have ten or more). This makes graduate students somewhat of a commodity, and most professors will put their graduate students on their hardest and most important projects. Most of the professors are very approachable, and a lot of them maintain open-door policies. The only really common complaint I hear from graduate students is concerning the class workload during their first two or three years. BYU doesn't have true tenure for their university, so even seasoned professors can get fired for being awful teachers. The consequence is that most of them have at least a passing interest in education research and regularly apply it in ways that often can be summed up with one thing: lots of really hard homework. (No, really. The grad student in my research group got his MS somewhere else and said that he loved the attention and care from the professors here but absolutely hated the amount of work they assigned.)
The university itself is run by the Church of Jesus Christ of Latter-day Saints. You don't have to be a member to attend, but most students and faculty are, and everyone is expected to agree to live an honor code regardless of religious affiliation. This makes the school very socially and somewhat politically conservative relative to what you would see at a typical institution. The religious affiliation does create some interesting quirks, too, such as the absence of coffee resulting in truly incredible levels of consumption of chocolate-flavored dairy beverages.

Research:
The department is pretty computationally heavy. Even a lot of the experimental professors dabble in computational modeling, and a few experimental undergraduates end up writing their senior theses about simulations and big software packages they developed for their experiments. There are very large groups in acoustics (somewhat of an oddity in a physics department, but it's a specialty here), condensed matter (which also includes the biophysics and materials science groups), and astronomy, but there are also very active groups in AMO and theoretical and mathematical physics. The plasma and nuclear groups are on their last legs, and you won't find much in the way of particle physics. Some particularly good groups include the computational materials science group led by Gus Hart and a group led by Darin Ragozzine on exoplanets and orbital dynamics.
My own personal interests are in theoretical gravitational physics, so my best information concerns the theory group. If you're interested in cutting-edge research on finding new physics beyond the Standard Model or exploring the mathematical intricacies of various gauge theories, you won't find much of that here, but there are very active groups in numerical relativity (particularly compact mergers and their emitted gravitational waves, but there are often side projects in black hole dynamics and relativistic fluids), quantum information and dynamics, and complex systems (if you're wondering what that entails, so do I; the group does everything from models of superconductivity to machine learning for acoustics problems to applied mathematics to simplify power grids and model biological systems).

Admissions:
Generally speaking, I would say admissions are pretty easy here relative to most graduate programs. A solid undergraduate GPA and a halfway decent GRE score should be enough to get most applicants in, so most people who survived their undergrad well enough to consider graduate school are probably okay.

Again, I'm a senior, not a grad student, so my perspective is that of an observer. Most of the graduate students I talk to say that they really enjoy their time here, and I don't think I've met any who feel like they're just slaves used to get more publications.